The fiercely private daughter of the nation’s 35th president, Ms. Kennedy is better known for her love of poetry and writing civic books for young adults than for any expertise in the rough-and-tumble political world.

But as an heir to one of America’s political dynasties, her urge for public service is not that surprising.

From her early years as a child living in the White House, to a lifetime of quietly campaigning for family, to her more recent prominent involvement with the Obama campaign, politics and public service have saturated the air around her.

“None of these people ever sat in a city council or served in the state Assembly,” says Mr. Zogby, whose polling firm is based in Utica, N.Y. “We have a tradition of choosing people who are larger than life. This is a Kennedy – at least she lives in New York.”

But not all New Yorkers are keen on the idea, primarily because of Kennedy’s lack of political experience.

The state and city face multibillion-dollar deficits. The financial sector, the engine that has kept the Big Apple running for the past quarter of a century, has stumbled badly. Some pols and pundits say what’s needed is experience and economic expertise to help New York rebuild its economy, not a celebrity.

“It would be a singularly inappropriate appointment,” says Fred Siegel at the Manhattan Institute, a conservative think tank. “She is someone who has no knowledge or interest in money and the underlying economic questions facing the state.”

The decision lies with Gov. David Paterson (D), who has the sole authority to appoint Senator Clinton’s successor and has to balance the political landscape in making his choice.He has some strong political alliances with other elected officials who have signaled their interested in Clinton’s seat. The most prominent is Attorney General Andrew Cuomo, another heir to a New York political dynasty. (His father Mario Cuomo was governor.) That has to be balanced against the star power and national fundraising potential of a Kennedy appointment.

“There may be a political and electorate payoff for Paterson in 2010 if [Kennedy] were on the ballot with him that he has to consider,” says pollster Lee Miringoff, director of the Marist Poll in Poughkeepsie, N.Y.

In a recent Marist Poll, Kennedy and Attorney General Cuomo were deadlocked at 25 percent each when New Yorkers were asked whom they’d like to see as the next senator. But that was before Kennedy expressed interest by reaching out to state political leaders this week.

Some of Senator Clinton’s prominent supporters have publicly opposed the idea of a Sen. Caroline Kennedy, citing her lack of experience.

“The irony of all ironies: every single word verbatim that the Clinton people are using against Caroline Kennedy [was] used against Hillary 10 years ago,” says Zogby.

When she first ran for the Senate, Clinton had a fairly steep learning curve. But she impressed many with her work ethic and especially her attention to Upstate, a relatively rural, conservative area.

“There will be a learning curve for Kennedy, as well,” says pollster Miringoff. “She has been around politics all of her life and has built-in appeal and name recognition, but being a candidate is a different ball game.”

Other critics wonder if Kennedy, with her seemingly gentle presence, has the grit to survive in New York’s sometimes brutal political culture. Her supporters point out that she’s a lawyer, a prominent fundraiser for the city’s schools, and a member of the board of many leading philanthropies. Then, of course, there’s the fact that she is a Kennedy.

“It’s grueling and brutal to have New York City pols going after you, which they are doing right now,” says Zogby. “Her father and uncle were assassinated and her brother killed in a plane crash. She’s been reading about herself and every family member in the tabloids for years. If anybody can handle New York politics, a Kennedy can.”